Graphical display techniques have been used on computers to allow the viewing of three-dimensional data on a two-dimensional viewing surface. Such graphical display techniques have been used in solids modeling and for viewing the results of finite element analysis and computational fluid dynamics, for example.
Solids modeling involves defining the geometry of an object to be displayed. Finite elements analysis involves the analysis of the physics of an object. Conventional methods of reviewing the results of finite elements analysis have included generating contour line plots for stress, color contour plots, and deformation and mode shape plots. Graphical display techniques for reviewing the results of computational fluid dynamics typically have used regular topology to define irregular geometry.
A limitation of many of the prior techniques for viewing three-dimensional results is that they display computed data only on the "visible outer surface" of the object. Unfortunately, "interesting" computed results do not always lie on the outer surface of a solid, but may in fact reside in its interior.
Prior three-dimensional viewing techniques have typically involved polygon clipping. A polygon is a closed plane figure having three or more sides. Polygon clipping refers to removing the portion of a given surface outside a given boundary. U.S. Pat. No. 3,816,726 of Sutherland et al. entitled COMPUTER-GRAPHICS CLIPPING SYSTEM FOR POLYGONS discloses a system for clipping three-dimensional polygons for use in a computer-graphics display. In particular, U.S. Pat. No. 3,816,726 discloses a technique for computing an intersection point between a line and a limiting plane.
U.S. Pat. No. 4,710,876 of Cline et al. entitled SYSTEM AND METHOD FOR THE DISPLAY OF SURFACE STRUCTURES CONTAINED WITHIN THE INTERIOR REGION OF A BOUNDED VOLUME BODY does disclose a method and apparatus for displaying surfaces contained within the interior regions of bounded volume bodies. U.S. Pat. No. 4,710,876 discloses the use of a voxel element defined by eight cubically-adjacent grid points. Said patent also discloses the use of a lookup table.
U.S. Pat. No. 4,694,404 of Meagher entitled HIGH-SPEED IMAGE GENERATION OF COMPLEX BOUNDED VOLUME OBJECTS USING OCTREE ENCODING discloses that areas of a view plane are tested to determine if they are completely enclosed by a projection, intersect but are not enclosed by the projection, or are completely disjoint with the projection. U.S. Pat. No. 4,694,404 discloses that areas that are completely enclosed by the projection are painted onto a display screen. Said patent discloses that areas which intersect but are not enclosed by the projection are further subdivided to locate those areas which are enclosed so that they, too, can be painted. Said patent discloses that the subdividing process continues until a predetermined degree of resolution is reached.